**Algebra**

**Question 1.Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.**

**Solution:**

Some possible expressions using three numbers 5, 7 and 8 are**(i)** 5 + (8 – 7)**(ii)** 5 -(8 – 7)**(iii)** 5 +(8 + 7)**(iv)** (5 + 8)+ 7**(v)** 5 x 8 + 7**(vi)** 5 x 7 + 8**(vii)** 5 x 8 – 7**(viii)** 5 x 7 – 8**(ix)** 5 x (8 – 7)**(x)** 5 x (8 + 7)**(xi)** 8 x (7 – 5)**(xii)** 8 x (7 + 5) etc.

**Question 2.Which out of the following are expressions with numbers only?**

**(a)**y + 3

**(b)**(7 x 20) – 8z

**(c)**5(21 – 7) + 7 x 2

**(d)**5

**(e)**3x

**(f)**5 – 5n

**(g)**(7 x 20) (5 x 10) – 45 + p

**Solution:**

(c) and (d) are expressions with numbers only.

**Question 3.Identify the operations (addition, subtraction, division, multiplication) in forming the following expressions and tell how the expressions have been formed:**

**(a)**z +1, z – 1 y +17, y -17

**(b)**17y, , 5z

**(c)**2y +17, 2y -17

**(d)**7m, -7m + 3, -7m – 3

**Solution:**

**Question 4.Give expressions for the following cases:**

**(a)**7 added to p

**(b)**7 subtracted from p

**(c)**p multiplied by 7

**(d)**p divided by 7

**(e)**7 subtracted from -m

**(f)**-p multiplied by 5

**(g)**-p divided by 5

**(h)**p multiplied by -5

**Solution:**

**Question 5.Give expressions in the following cases:**

**(a)**11 added to 2m

**(b)**11 subtracted from 2m

**(c)**5 times y to which 3 is added

**(d)**5 times y from which 3 is subtracted

**(e)**y is multiplied by -8

**(f)**y is multiplied by -8 and then 5 is added to the result

**(g)**y is multiplied by 5 and the result is subtracted from 16

**(h)**y is multiplied by -5 and the result is added to 16

**Solution:**

**Question 6.****(a)** Form expressions using t and 4. Use not more than one number operation. Every expression must have t in it.**(b)** Form expressions using y, 2 and 7. Every expression must have y in it. Use only two number operations. These should be different.

**Solution:****(a)** Possible expressions using t and 4 are

t + 4, t – 4, 4t and .**(b)** Possible expressions using y, 2 and 7 (having only two different number operations) are

2y + 7, 2y – 7, 7y + 2, 7y – 2, + 7, – 7, +2 and – 2.